Exchange narrowing in circular and cylindrical molecular aggregates: degenerate versus nondegenerate states

We study the optical absorption line shape of circular and cylindrical molecular aggregates with static Gaussian diagonal and off-diagonal disorder. We focus on the weak-disorder situation and analyze the effect of exchange nar-rowing of the disorder due to exciton delocalization. In particular, we show that the absorption lines originating from pairs of states that are degenerate in the ordered aggregate (e.g., the k 1 pair in rings) is always broader than the one originating from a nondegenerate state. If we only account for diagonal disorder, this difference amounts to a factor offfiffiffi 2 p. Moreover, in contrast to the nondegenerate case, the degenerate states give rise to a nonGaussian absorption profile that may even reflect its origin in two states through the emergence of a double-peak structure. The latter occurs if the off-diagonal disorder dominates and if the circumference of the ring or the cylinder is small enough (<8 mole-cules). 2002 Elsevier Science B.V. All rights reserved. 1